Methods for statistical prediction of well production and reserves

ABSTRACT

A method for optimizing a well production forecast includes a) inputting initial production rate measurements made at selected times, b) inputting probability distributions to estimate production forecast model parameters, c) generating an initial forecast of fluid production rates and total produced fluid volumes using a selected production forecast model, d) at a time after a last one of the selected times, comparing the initial forecast with actual production rate and total produced fluid volume measurements to generate an error measurement, e) adjusting parameters of the selected production forecast model to minimize the error measurement, thereby generating an adjusted production forecast model, f) repeating (d) and (e) for a plurality of iterations to generate a plurality of production forecast models each having a determined likelihood of an error measurement and displaying the plurality of production forecast models with respect to likelihood of error.

BACKGROUND

This disclosure is related to the field of analysis of fluid productionfrom subsurface wellbores to evaluate expected future fluid productionand ultimate total fluid production therefrom. More specifically, thedisclosure relates to methods for statistical analysis of time-dependentfluid production rate and cumulative produced fluid volume measurementsto obtain improved estimates of future fluid production rate andultimate cumulative production volumes.

Statistical prediction of well fluid production rates is known in theart for use in estimating wellbore reserves and wellbore economic value.Several methods known in the art are used to quantify the uncertainty inwellbore fluid production forecasts, which is useful for representing arange of reserves in accordance with United States Securities andExchange Commission (SEC) reserves reporting rules, and estimating thechance of commercial success of oil and gas wells given the inherentuncertainty in forecasting.

Production forecasts are engineering interpretations of fluid productionvolumetric or mass rate data to predict the performance of hydrocarbonproducing (oil and gas) wells. Data used for production forecasts may beobtained from disparate sources, but most often when a wellbore isalready producing fluids (including oil and/or gas), the data used aretypically solely measurements of production rates. The fluid productionrate is often displayed on a Cartesian coordinate graph wherein thefluid production rate is shown on the y-axis, and the time ofmeasurement shown on the x-axis. An example fluid production rate graphis shown in FIG. 1. Many different versions of the same basic datadisplay also known in the art to be used, such as log-log and semi-logaxis display of the same fluid production rate data (shown in FIG. 2 andFIG. 3), as well as other transforms of the fluid production rate data.These manipulations and transforms may identify different trends used tocharacterize the change in fluid production rate over time, and toevaluate the quality of the fit of a model to the fluid production ratemeasurement data. A model may be a representation of inferred physicalcharacteristics of a particular subsurface reservoir, such as fluidpressure, fractional volumes of pore space occupied by oil, gas andwater, viscosities and composition of the reservoir fluids, geometry ofthe reservoir, and the drive mechanism by which fluid is moved from thereservoir to the Earth's surface.

Interpretation of the fluid production rate measurement data to generatea fluid production rate and/or cumulative produced fluid volume forecastis usually performed by analysis of the interpreter in a process of“tuning ” Estimates of the parameters used in the model used forforecasting may be obtained from interpretation or diagnosis of thefluid production rate measurement data, or, when the data displays nostrong indications, from analogous data such as data from geodeticallyproximate (“offset”) wells or subsurface reservoirs having similarcharacteristics. For example, a wellbore having a well-defined fluidproduction rate measurement trend is shown in FIG. 4, while a wellborehaving fluid production rate measurement data that may be characterizedas “noisy” is shown in FIG. 5.

Interpretation of fluid production rate measurement data using knowntechniques such as curve fitting to generate fluid production rateforecasts and/or cumulative fluid production volume forecasts typicallydoes not include a calculation of error between the forecast and themeasurement data. Such forecasts are typically performed by a humaninterpreter and are based at least in part on informed but subjectivejudgment of the human interpreter. There are limitations associated withforecasting based on such human interpretation including, for example,difficulties associated with consistently reproducing interpretationsamong different human interpreters, non-uniqueness of interpretationsamong interpreters, the inability to rapidly make interpretations usingcomputer algorithms, the inability to quantify the uncertainty inherentin any prediction of future well production, and the requirement thatthe interpreter be highly skilled in the art of fluid production ratemeasurement data interpretation so as to make subjective judgments wellinformed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a graph of production data with production rate on they-axis, and the time of measurement on the x-axis in Cartesiancoordinates.

FIG. 2 shows a graph such as in FIG. 1 with a logarithmic scale on they-axis.

FIG. 3 shows a graph such as in FIG. 1 with a logarithmic scale on bothaxes.

FIG. 4 shows a graph such as FIG. 1 for an example well having awell-defined production decline trend with respect to time.

FIG. 5 shows a graph such as FIG. 1 for an example well having what maybe described as a “noisy” production rate with respect to time.

FIG. 6 shows a histogram of distribution of accepted model proposalsranked by estimated ultimate recovery (EUR).

FIG. 7 shows a cumulative distribution function of accepted modelproposals ranked by EUR.

FIG. 8 shows P90, P50, & P10 percentile neighborhood productionforecasts.

FIG. 9 shows mean percentile neighborhood production forecast.

FIGS. 10A, 10B and 10C show a flow chart of an example method accordingto the present disclosure.

FIG. 11 shows an example computer system for performing analysisaccording to the present disclosure.

DETAILED DESCRIPTION

In performing analysis methods according to the present disclosure, atselected times a rate of fluid production from a wellbore is measured.The fluid production rate measurements may include measurements of anyor all of volumetric and/or mass flow rates of gas, water and oil. Gasproduction may be quantified volumetrically in units of thousands ofstandard cubic feet per day (wherein the volume of gas is corrected tothe volume it would occupy at “standard’ conditions of 25 degrees C. anda pressure of 1 bar), Oil and water production may be quantifiedvolumetrically in barrels per day (1 barrel is equal to 42 U.S.gallons). The fluid production rate measurements may be entered into acomputer or computer system for processing as will be explained furtherwith reference to FIGS. 10 and 11.

In analysis methods according to the present disclosure, certainparameters and attributes may be defined. The first nine attributeslisted below correspond to a specific production forecast model whichmay be used in some embodiments. In the present example embodiment theTransient Hyperbolic Model (described below) may be used. Differentproduction forecast models may be used in other embodiments; such otherproduction forecast models may require substitution of or modificationof some or all of the below listed attributes for the respectiveproduction forecast model's specific parameters.

1. Initial Rate Attribute: This attribute is the initial fluidproduction rate of the model, written as the parameter q₁.

2. Initial Decline Attribute: This attribute is the initial fluidproduction decline rate used for the production forecast model,expressed herein as the parameter D_(i).

3. Initial Hyperbolic (b-) Parameter Attribute: This attribute is theinitial hyperbolic parameter of the production forecast model, alsoreferred to as the b-parameter, hyperbolic exponent, or n-exponent. Itis expressed herein as the parameter b_(i).

4. Final Hyperbolic Parameter Attribute: This attribute is the finalhyperbolic parameter of the production forecast model, expressed hereinas the parameter b_(f).

5. Time to End of Linear Flow Attribute: This attribute is the time tothe end of linear flow of the production forecast model, expressedherein as the parameter t_(etf).

6. Distribution of Initial Decline Attribute: This attribute is anestimate of a range of possible values for the Initial DeclineAttribute. This attribute constrains randomly generated productionforecast models and production forecast model parameters to withinboundaries determined, by, for example, expert opinion (i.e., informed,subjective human judgment), allowing for more accurate fluid productionforecasts. Any type of distribution may be used. In some embodiments auniform distribution is used.

7. Distribution of final b-parameter Attribute: This attribute is anestimate of the range of possible values for the b-parameter. Thisattribute constrains randomly generated models and model parameters towithin boundaries determined, by, for example, expert opinion (i.e.,informed, subjective human judgment), allowing for more accurate fluidproduction forecasts. Any type of distribution may be used. In someembodiments a uniform distribution is used.

8. Distribution of time to end of linear flow (0 Attribute: Thisattribute is an estimate of a range of possible values for the t_(eif)parameter. This attribute constrains randomly generated models and modelparameters to within boundaries determined, by, for example, expertopinion (i.e., informed, subjective human judgment), allowing for moreaccurate fluid production forecasts. Any type of distribution may beused. In some embodiments a log-normal distribution is used.

9. Prior Likelihood of Model Parameter Attribute: This attribute is thelikelihood of any model parameter represented by a probabilitydistribution. This attribute is useful for measuring likelihood of anyfluid production model parameter given an expert opinion (i.e., aninformed, subjective human judgment) of the fluid production modelparameter's distribution. For a uniform probability distribution, thelikelihood is normalized by itself and therefore expresses nosubstantial indication of the likelihood of any parameter value withinbounds of the distribution, but only that the fluid production modelparameter must fall within the bounds expressed. This is referred to asan uninformative prior. For a parameter in which an informative prior isused as a distribution, such as the time to end of linear flowattribute, this attribute is defined as:

${\pi \left( {\left. \theta \middle| q_{i} \right.,D_{i},b_{i},b_{f},t_{elf}} \right)} = {\frac{1}{\sqrt{2\pi}t_{elf}\sigma_{t_{elf}}}^{- \frac{{({{L\; {N(t_{elf})}} - \mu_{t_{elf}}})}^{2}}{2\sigma_{t_{{elf}^{2}}}}}*\ldots \mspace{14mu} {etc}}$

Using the likelihood of the time to end of linear flow parameter as anexample for the prior likelihood, the prior likelihood may besubstituted for any fluid production model parameter, as well as theproduct of likelihood of multiple fluid production model parameters.

The following attributes are general to the present disclosure and arenot related to any specific production forecast model that may be used.

10. Logarithm Residuals Attribute: This attribute evaluates thelogarithm residuals between the input data (the fluid production ratemeasurements with respect to time) and the values of fluid productionwith respect to time calculated by a specific fluid production forecastmodel at corresponding values of time. The logarithm residuals may beevaluated for every fluid production rate input data point (i.e., thefluid production rate measurements and time at which the measurementswere made), and may be expressed as:

ε=ln(data)−ln(model)

11. Standard Deviation of Logarithm Residuals Attribute: This attributeis a measure of the standard deviation of the above described logarithmresiduals, ε. This attribute is useful for measuring a difference incurvature between the input data and the forecast values for anyparticular fluid production forecast model. This attribute may beexpressed as:

$\sigma_{ɛ} = \sqrt{\frac{1}{n - 1}{\sum\limits_{i = 1}^{n}\left( {ɛ_{i} - \overset{\_}{ɛ}} \right)^{2}}}$

where n represents the number of input data points being evaluated, andε is the logarithm residual. ε represents the average of all values oflogarithm residuals.

12. Minimum Standard Deviation of Logarithm Residuals Attribute: Thisattribute is the minimum standard deviation of logarithm residualsdetermined during the evaluation of any particular fluid productionforecast model. This attribute may be determined by means of a geneticalgorithm as each of a plurality of fluid production forecast models israndomly generated from a prior “accepted” (defined below) fluidproduction forecast model. The attribute may be expressed as:

σ_(ε) _(min) =min[σ_(ε)]

13. Distribution of Standard Deviation of Logarithm Residuals Attribute:This attribute represents the distribution of the standard deviation oflogarithm residuals between the input data and the values calculated bya particular fluid production forecast model. The distribution isassumed to be a normal distribution, with a standard deviationempirically tuned for an optimum rate of acceptance of fluid productionforecast models generated, e.g., randomly. This attribute may beexpressed as as:

θ_(ε)˜

(σ_(ε) _(min) , 0.01)

14. Likelihood of Standard Deviation of Logarithm Residuals Attribute:This attribute evaluates the likelihood of the standard deviation oflogarithm residuals as a function of the normal distribution with a meanof the minimum standard deviation of logarithm residuals, and standarddeviation of 0.01. The attribute may be expressed as:

${f\left( \theta_{ɛ} \middle| \sigma_{ɛ} \right)} = {\frac{1}{\sqrt{2\pi}}^{{- \frac{1}{2}}{(\frac{{({\sigma_{ɛ} - \sigma_{ɛ_{\min}}})}^{2}}{0.01^{2}})}}}$

15. Magnitude of Logarithm Residuals Attribute: This attribute evaluatesthe magnitude of logarithm residuals between the input data and thevalues calculated by any particular fluid production forecast model. Themagnitude of logarithm residuals may be evaluated for every input datapoint, and are defined as:

ε=abs[LN(data)−LN(model)]

16. Mean of Magnitude of Logarithm Residuals Attribute: This attributeis a measure of the arithmetic mean of the logarithm residuals, ε. Thisattribute is useful for measuring the absolute error between the inputdata and the values calculated using an particular fluid productionforecast model. The attribute may be expressed as:

μ_(ε)=ε

where ε is the magnitude of the logarithm residual.

17. Minimum Mean of Magnitude of Logarithm Residuals Attribute: Thisattribute is the minimum mean of logarithm residuals measured during theevaluation of any particular fluid production forecast model. Thisattribute may be determined by means of a genetic algorithm as eachfluid production forecast model is randomly generated from a prioraccepted fluid production forecast model. The attribute may be expressedas:

μ_(ε) _(min) [μ_(ε)]

18. Distribution of Mean of Magnitude of Logarithm Residuals Attribute:This attribute describes the distribution of the mean of magnitude oflogarithm residuals between the data and the model fluid production rateforecast. The distribution is assumed to follow a normal distribution,with a standard deviation empirically tuned for an optimum acceptancerate of possible fluid production forecast models, e.g., as generatedrandomly from a prior accepted fluid production forecast model. Theattribute may be expressed as:

θ_(ε)˜

(μ_(ε) _(min) , 0.1)

19. Likelihood of Mean of Magnitude of Logarithm Residuals Attribute:This attribute evaluates the likelihood of the mean of magnitude oflogarithm residuals as a function of the normal distribution with a meanof the minimum mean of magnitude of logarithm residuals, and standarddeviation of 0.1. The attribute may be expressed as:

${f\left( \theta_{\varepsilon} \middle| \mu_{\varepsilon} \right)} = {\frac{1}{\sqrt{2\pi}}^{{- \frac{1}{2}}{(\frac{{({\mu_{\varepsilon} - \mu_{\varepsilon_{\min}}})}^{2}}{0.1^{2}})}}}$

20. Likelihood of Model Proposal Attribute: This attribute evaluates thelikelihood that a particular fluid production forecast model is anacceptable description of the fluid production rate measurements (i.e.,the input data). The attribute may be expressed as:

${f\left( {\left. \theta \middle| \sigma_{ɛ} \right.,\mu_{\varepsilon}} \right)} = {\frac{1}{2\pi}^{{- \frac{1}{2}}{({\frac{{({\sigma_{ɛ} - \sigma_{ɛ_{\min}}})}^{2}}{0.01^{2}} + \frac{{({\mu_{\varepsilon} - \mu_{\varepsilon_{\min}}})}^{2}}{0.1^{2}}})}}*{\pi \left( {\left. \theta \middle| q_{i} \right.,D_{i},b_{i},b_{f},t_{elf}} \right)}}$

21. Model Acceptance Attribute: This attribute uses the “Metropolis”algorithm to evaluate the acceptance probability of any particular fluidproduction forecast model. Each fluid production forecast model isaccepted with probability normalized by the likelihood of the prioraccepted fluid production forecast model. If the current fluidproduction forecast model is more likely, it is accepted. Otherwise thefluid production forecast model is accepted with a determinable ordetermined probability. The attribute may be expressed as:

$\alpha = {\min \left( {1,\frac{{f(\theta)}{\pi (\theta)}}{{f\left( \theta_{i - 1} \right)}{\pi \left( \theta_{i - 1} \right)}}} \right)}$

where α is the acceptance probability, θ is the current model proposal,and θ_(i−1) is the prior accepted fluid production forecast model.

22. Distribution of Accepted Model Proposals Attribute: This attributeis the result of the evaluation and acceptance of fluid productionforecast models from the fluid production forecast model acceptanceattribute. This attribute is the set of possible forecasts, referred toas the statistical distribution of well performance.

23. Histogram of Distribution of Accepted Model Proposals Attribute: Ahistogram or “density function” of the distribution of accepted fluidproduction forecast models, after ranking by expected ultimate recovery(EUR). This attribute is useful for illustrating the likelihood of theEUR from the accepted fluid production forecast models, and can beobserved in FIG. 6.

24. Cumulative Distribution Function of Accepted Model ProposalsAttribute:

The cumulative distribution function of the distribution of acceptedfluid production forecast models, after ranking by EUR. This attributeis useful for illustrating the percentiles of the distribution ofaccepted fluid production forecast models, and can be seen in FIG. 7.

25. Production Forecast of Percentile Neighborhood Attribute: Theforecast of a given percentile neighborhood represents features from aplurality accepted fluid production forecast model, as well as thepossible accepted fluid production forecast models that are notgenerated due to limiting the number of iterations in the simulation forthe purpose of reducing calculation time. At each percentile ofinterest, a production forecast representative of the features of aplurality of forecasts proximate the given percentile (hence “percentileneighborhood”) is created by averaging each parameter of the fluidproduction forecast model among all iterations in the neighborhood. Aneighborhood size of +/−1 percentile is typically chosen. The 10^(th),50^(th), and 90^(th) percentiles, referred to as P90, P50, and P10,respectively, are typically chosen for a simplified representation ofthe full distribution of production forecasts, although any percentilemay be chosen. Examples of P90, P50, and P10 forecasts are shown in FIG.8. The mean forecast is determined as the percentile neighborhood'sforecast which results in the mean EUR. An example of a mean forecast isshown in FIG. 9.

Methods according to the present disclosure may use, without limitation,any of the following methods that may be advantageously applied forstatistical prediction of fluid production rates, including but notlimited to the attributes described above:

26. Markov Chain Monte Carlo Method: This method utilizes a Markov chainto generate random model proposals for evaluation of likelihood ofacceptance for the set of possible fluid production rate forecasts.

27. Production Forecast Method: This method uses a production forecastto calculate an expected time-dependent array of fluid production rates.The results of any forecast are referred to as the “fluid productionforecast model”. While any production forecast model may be used, in thepresent example implementation, the Transient Hyperbolic Model is used.

28. Expected Ultimate Recovery Integral Method: This method evaluatesthe integral of the rate-time array of fluid production rates from afluid production forecast model to forecast the EUR for such fluidproduction forecast model.

29. Rank of Accepted Model Proposals Method: This method ranks the setof fluid production forecast models by the EUR to evaluate the chancethat the EUR of the fluid production forecast models exceed a value ofinterest. This method is useful for reporting the confidence interval ofEUR for the production data that has been analyzed.

Referring to FIGS. 10A, 10B and 10C, an example well fluid productionrate analysis method according to the present disclosure will now beexplained. In FIG. 10 A, at 10, fluid production rate measurements withrespect to time (i.e., the elapsed time since initiation of fluidproduction from a wellbore) may be input to a computer or computersystem (FIG. 11) programmed to perform a method as described herein. At12, prior beliefs (e.g., subjective human interpretations) of fluidproduction forecast model parameters are input to the computer orcomputer system. The prior beliefs may be represented by attributes 6through 8 listed above. At 14, random values of parameters for a fluidproduction rate forecast model for an initial simulation iteration (thisis the initial fluid production forecast model and may be represented byparameters 1-5 above) are entered into the computer or computer system.

At 16, a fluid production rate forecast is generated by the computer orcomputer system. The fluid production rate forecast may be attribute 27described above in the present implementation. At 18, differences(errors) between the fluid production rate forecast and the input datafluid production rate measurements (at the time(s) of the measurements)are calculated. The errors may be expressed by attributes 10, 11, 15 and16 described above At 20, the errors may be stored in the computer orcomputer system as minimum errors, for example as attributes 12 and 17set forth above. At 22, the likelihood of a fluid production forecastmodel relative to minimum errors may be determined by the computer orcomputer system. This may be performed by the computer or computersystem using attributes 12-14 and 18-20 as set forth above.

In FIG. 10B, at 24, an iterative process, using, for example, the MarkovChain

Monte Carlo method (attribute 26 as set forth above) may be initiated.At 24A, parameters of a fluid production rate forecast generated using arandom walk from a prior accepted fluid production rate forecast modelare generated by the computer or computer system. At 24B, a fluidproduction rate forecast may be generated, e.g., using model attribute27 as set forth above. At 24C, errors between the fluid production rateforecast and the input data are calculated by the computer or computersystem as attributes 10, 11, 15 and 16 set forth above. At 24D, if thecurrent iteration errors are smaller than the previous iteration errors,the current iteration errors are stored in the computer or computersystem. At 24E, a likelihood of the fluid production rate forecast modelrelative to minimum error is calculated by the computer or computersystem.

At 24F, acceptance probability as likelihood relative to the prioraccepted fluid production rate forecast model is calculated in thecomputer or computer system This may be performed using attribute 21 setforth above. At 24G, the fluid production rate forecast model isaccepted or rejected, which may be based on attribute 22 as set forthabove. At 24J, if the fluid production rate forecast model is accepted,it becomes the “prior” accepted fluid production rate forecast mode in asubsequent iteration. If the fluid production rate forecast model isrejected, then the most recent accepted fluid production rate forecastmodel is retained as the “prior” accepted model proposal, e.g., asevaluated using attribute 22 given above.

In FIG. 10C, at 26, a selected number, n, of fluid production rateforecast models may be discarded during an initialization period inwhich convergence to a selected number of fluid production rate forecastmodels is obtained, which may be referred to as the “posteriordistribution.” At 28, an EUR may be calculated for all iterations of allaccepted fluid production rate forecast models. At 30, a fluidproduction rate forecast model distribution may be sorted by EUR. At 32,the percentiles of the fluid production rate forecasts may be generatedin the computer or computer system using attribute 25 set forth above.At 34 and 36, respectively, a histogram and cumulative distribution plotsorted by EUR of the selected fluid production rate forecast models maybe generated by the computer or computer system. At 38, fluid productionrate forecasts from all iterations may be displayed, e.g. on a graphiccomputer user interface.

FIG. 11 shows an example computing system 100 in accordance with someembodiments. The computing system 100 may be an individual computersystem 101A or an arrangement of distributed computer systems. Theindividual computer system 101A may include one or more analysis modules102 that may be configured to perform various tasks according to someembodiments, such as the tasks explained with reference to FIG. 10. Toperform these various tasks, the analysis module 102 may operateindependently or in coordination with one or more processors 104, whichmay be connected to one or more storage media 106. A display device 105such as a graphic user interface of any known type may be in signalcommunication with the processor 104 to enable user entry of commandsand/or data and to display results of execution of a set of instructionsaccording to the present disclosure.

The processor(s) 104 may also be connected to a network interface 108 toallow the individual computer system 101 A to communicate over a datanetwork 110 with one or more additional individual computer systemsand/or computing systems, such as 101 B, 101C, and/or 101D (note thatcomputer systems 101B, 101C and/or 101D may or may not share the samearchitecture as computer system 101A, and may be located in differentphysical locations, for example, computer systems 101A and 101B may beat a well drilling location, while in communication with one or morecomputer systems such as 101C and/or 101D that may be located in one ormore data centers on shore, aboard ships, and/or located in varyingcountries on different continents).

A processor may include, without limitation, a microprocessor,microcontroller, processor module or subsystem, programmable integratedcircuit, programmable gate array, or another control or computingdevice.

The storage media 106 may be implemented as one or morecomputer-readable or machine-readable storage media. Note that while inthe example embodiment of FIG. the storage media 106 are shown as beingdisposed within the individual computer system 101A, in someembodiments, the storage media 106 may be distributed within and/oracross multiple internal and/or external enclosures of the individualcomputing system 101A and/or additional computing systems, e.g., 101B,101C, 101D. Storage media 106 may include, without limitation, one ormore different forms of memory including semiconductor memory devicessuch as dynamic or static random access memories (DRAMs or SRAMs),erasable and programmable read-only memories (EPROMs), electricallyerasable and programmable read-only memories (EEPROMs) and flashmemories; magnetic disks such as fixed, floppy and removable disks;other magnetic media including tape; optical media such as compact disks(CDs) or digital video disks (DVDs); or other types of storage devices.Note that computer instructions to cause any individual computer systemor a computing system to perform the tasks described above may beprovided on one computer-readable or machine-readable storage medium, ormay be provided on multiple computer-readable or machine-readablestorage media distributed in a multiple component computing systemhaving one or more nodes. Such computer-readable or machine-readablestorage medium or media may be considered to be part of an article (orarticle of manufacture). An article or article of manufacture can referto any manufactured single component or multiple components. The storagemedium or media can be located either in the machine running themachine-readable instructions, or located at a remote site from whichmachine-readable instructions can be downloaded over a network forexecution.

It should be appreciated that computing system 100 is only one exampleof a computing system, and that any other embodiment of a computingsystem may have more or fewer components than shown, may combineadditional components not shown in the example embodiment of FIG. 11,and/or the computing system 100 may have a different configuration orarrangement of the components shown in FIG. 11. The various componentsshown in FIG. 11 may be implemented in hardware, software, or acombination of both hardware and software, including one or more signalprocessing and/or application specific integrated circuits.

Further, the acts of the processing methods described above may beimplemented by running one or more functional modules in informationprocessing apparatus such as general purpose processors or applicationspecific chips, such as ASICs, FPGAs, PLDs, or other appropriatedevices. These modules, combinations of these modules, and/or theircombination with general hardware are all included within the scope ofthe present disclosure.

While the invention has been described with respect to a limited numberof embodiments, those skilled in the art, having benefit of thisdisclosure, will appreciate that other embodiments can be devised whichdo not depart from the scope of the invention as disclosed herein.Accordingly, the scope of the invention should be limited only by theattached claims.

What is claimed is:
 1. A method for optimizing a well productionforecast, comprising: a) inputting fluid production rate measurementsmade at selected times into a computer; b) inputting probabilitydistributions related to a likelihood of a plurality of fluid productionrate forecast model parameters into the computer; c) in the computergenerating an initial forecast of fluid production rates and totalproduced fluid volumes using a selected fluid production forecast model;d) at a time after a last one of the selected times, in the computercomparing the initial forecast with the fluid production ratemeasurements and total produced fluid volume measurements to generate anerror measurement; e) in the computer accepting or rejecting theselected production forecast model based upon a likelihood of the errormeasurement relative to a prior forecast model and a likelihood of fluidproduction rate forecast model parameters; f) in the computer, randomlyadjusting parameters of the selected fluid production rate forecastmodel to minimize the error measurement, thereby generating an adjustedfluid production rate forecast model; g) in the computer, repeating (d),(e), and (f) for a plurality of iterations to generate a plurality offluid production rate forecast models each having a determinedlikelihood of error; and h) displaying the plurality of fluid productionrate forecast models with respect to the likelihood of error.
 2. Themethod of claim 1 wherein the selected production forecast model isbased on a Markov Chain Monte Carlo Method.
 3. The method of claim 1wherein the plurality of fluid production rate forecast model parameterscomprise one or more of (i) an initial fluid production rate of themodel, (ii) an initial fluid production decline rate, (iii) an initialhyperbolic parameter of the production forecast model, (iv) a finalhyperbolic parameter of the production forecast model, and (v) a time toan end of linear flow of the production forecast model.
 4. The method ofclaim 3 wherein the plurality of fluid production rate forecast modelparameters are constrained by one or more of (i) an estimate of a rangeof possible values of the initial fluid production decline rate, (ii) adistribution of the final hyperbolic parameter, (iii) a distribution ofthe time to the end of linear flow, and (iv) a likelihood of any modelparameter being represented by a probability distribution.